Related papers: Simultaneous stabilization, avoidance and Goldberg…
We investigate a few problems in the theory of linear time-invariant systems that arise when the open-loop system possesses imaginary eigenvalues. The problems are: (1) the infinite horizon, minimum energy optimal control problem; (2) the…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability which were introduced in previous papers. The paper presents a new geometric characterization of the…
Families of regimes for control systems are studied possessing the so called quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the degree of transients overshooting…
We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an order $p\in\mathbb N$, are bounded by prescribed values. We propose a static…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…